US 20030105868 A1 Abstract A benefit task system implements a policy for allocating resources to yield some benefit. The method implemented may be applied to a variety of problems, and the benefit may be either tangible (e.g., profit) or intangible (e.g., customer satisfaction). In one example, the method is applied to server allocation in a Web site server “farm” given full information regarding future loads to maximize profits for the Web hosting service provider. In another example, the method is applied to the allocation of telephone help in a way to improve customer satisfaction. In yet another example, the method is applied to distributed computing problem where the resources to be allocated are general purpose computers connected in a network and used to solve computationally intensive problems. Solution of the Web server “farm” problem is based on information regarding future loads to achieve close to the greatest possible revenue based on the assumption that revenue is proportional to the utilization of servers and differentiated by customer class. The method of server allocation uses an approach which reduces the Web server farm problem to a minimum-cost network flow problem, which can be solved in polynomial time. Similar solutions are applicable to other resource allocation problems.
Claims(15) 1. A method of resource allocation to yield a benefit comprising the steps of:
generating an input time-customer matrix of demands for resources where a benefit function is known in advance; and producing from the input matrix an output time-customer matrix of allocations of resources to customers to realize a benefit. 2. The method of resource allocation as recited in 3. The method of resource allocation as recited in 4. The method of resource allocation as recited in 5. The method of resource allocation as recited in 6. The method of resource allocation as recited in 7. The method of resource allocation as recited in 8. A method of resource allocation to yield a benefit comprising the steps of:
choosing a state s _{i}, for each time t so as yield a benefit where all the state sets and the benefit function are known in advance; reducing the problem to the analogous maximum-cost network flow problem by
constructing a directed network with s “rails”, one per site, each rail being a chain of edges each representing one time step, flow along a rail representing an allocation of resources to a corresponding site,
constructing a set of “free pool” nodes, one per time step, through which flow will pass when resources are reallocated from one site to another,
for a demand matrix d
_{i, t}, 1≦i≦s, 1≦t≦T, constructing nodes n_{i, t}, 1≦i≦s, 0≦t≦T, along with nodes f_{t}, 1≦t≦T, and for each site s and each time step t, constructing three edges from n_{i, t−1 }to n_{i, t}, wherein the first edge has capacity └d_{i, t}┘ and cost r_{i, t}, the second edge has capacity one and cost r_{i, t}·(d_{i, t}−└d_{i, t}┘), and the third edge has infinite capacity and cost zero, flow along the first edge representing a benefit of allocating resources s to site i during time step t, up to the integer part of d_{i, t}, flow along the second edge representing a remaining benefit, r_{i, t}, times a fractional part of d_{i, t }to be collected by one more resource, and flow along the third edge representing that extra resources can remain allocated to s but do not collect any benefit, constructing edges of infinite capacity and cost zero from n
_{i, t−1 }to f_{t }and from f_{i }to n_{i, t}, for each 1≦t≦T and each 1≦i≦s which represent a movement of servers from one site to another, constructing a source into which a flow k is injected, with infinite capacity zero cost edges to each n
_{i, 0}, and a sink with infinite capacity zero cost edges from each n_{i, T}; and solving the maximum-cost network flow problem and allocating resources.
9. The method of resource allocation as recited in 10. The method of resource allocation as recited in 11. The method of resource allocation as recited in 12. The method of resource allocation as recited in 13. The method of resource allocation as recited in 14. The method of resource allocation as recited in 15. A method for server allocation in a Web server “farm” based on information regarding future loads to achieve close to greatest possible revenue based on an assumption that revenue is proportional to the utilization of servers and differentiated by customer class comprising the steps of:
modeling the server allocation problem mathematically;
in the model, dividing time into intervals of fixed length based on the assumption that each site's demand is uniformly spread throughout each such interval;
maintaining server allocations fixed for the duration of an interval, servers being reallocated only at the beginning of an interval, and a reallocated server being unavailable for the length of the interval during which it is reallocated providing time to “scrub” the old site (customer data) to which the server was allocated, to reboot the server and to load the new site to which the server has been allocated, each server having a rate of requests it can serve in a time interval and customers share servers only in the sense of using the same servers at different times, but do not use the same servers at the same time;
associating each customer's demand with a benefit gained by the service provider in case a unit demand is satisfied and finding a time-varying server allocation that would maximized benefit gained by satisfying sites' demand; and
reducing to a minimum-cost network flow problem and solving in polynomial time.
Description [0001] 1. Field of the Invention [0002] The present invention generally relates to benefit task systems and, more particularly, to a policy for allocating resources to maximize some benefit. The invention may be applied to a variety of problems, and the benefit may be either tangible (e.g., profit) or intangible (e.g., customer satisfaction). In a specific example, the invention has particular application to server allocation in a Web site server “farm” given full information regarding future loads to maximize profits for the Web hosting service provider. In another specific example, the invention can be applied to the allocation of telephone help in a way to improve customer satisfaction. In yet another example, the invention may be applied to distributed computing problems where the resources to be allocated are general purpose computers connected in a network and used to solve computationally intensive problems. [0003] 2. Background Description [0004] Web content hosting is an important emerging market. Data centers and Web server “farms” are proliferating. The rationale for using such centers is that service providers can benefit from economies of scale and sharing of resources among multiple customers. This benefit in turn translates to lower cost of maintenance for the customers who purchase these hosting services. Web content hosting services are structured in many ways. One of the most prevailing ways is outsourcing: the customers deliver their Web site content in response to HTTP (hyper text transfer protocol) requests. Service providers will use “farms” of commodity servers to achieve this goal. [0005] One of the components in the payment for such a service is “pay per served request”. Thus, one of the main objectives of the service provider is to maximize the revenue from served requests while keeping the tab on the amount of resources used. Ideally, the allocation to a Web site should always suffice to serve its requests. However, due to a limited number of servers and the overhead incurred in changing the allocation of a server from one site to another, the system may become overloaded, and requests may be left unserved. Under the assumption that requests are not queued, a request is lost if it is not served at the time it is requested. The problem faced by the Web hosting service provider is how to utilize the available servers in the most profitable way, given full information regarding future loads. [0006] Similar considerations apply in the cases of computer servers and telephone support centers. Telephone support centers typically are computer controlled telephone networks having a number of technical support, order support and customer service support operators. These operators are resources that must be allocated to customers who call in. Computer software is used to answer telephone calls and direct the calls to the appropriate pool of operators. In this application, the operators are the resources to be allocated. The wait time that a customer experiences is inversely proportional to customer satisfaction and, therefore, it is important to allocate resources in such a manner as to minimize customer wait time and increase customer satisfaction. In this application, customer benefit is the intangible benefit which is sought to be maximized. [0007] In yet another example, the resources to be allocated are general purpose computers used to solve computationally intensive problems. In this environment, multiple computers can be used concurrently to solve a problem faster than a single computer can solve it. The computers would be connected in a network which may include the Internet. It has even been proposed that personal computers connected to the Internet might constitute resources that could be employed in solving such problems. It is anticipated that a market for such services will become standardized to some extent, so that the computer cycles become a commodity (resource) available from multiple vendors. [0008] It is therefore an object of the present invention to provide a method for resource allocation given full information regarding future requirements. [0009] It is another object of the invention to provide a method for resource allocation to achieve close to the greatest possible benefit based on the assumption that benefit is proportional to the utilization of resources. [0010] A method of resource allocation is based on a minimum-cost network flow problem, which can be solved in polynomial time. In the practice of the invention, the resource allocation problem is modeled mathematically. In the model, time is divided into intervals. For the Web server farm problem, the assumption is made that each site's demand is uniformly spread throughout each such interval. Server allocations remain fixed for the duration of an interval. It is also assumed that servers are reallocated only at the beginning of an interval, and that a reallocated server is unavailable for the length of the interval during which it is reallocated. This represents the time to “scrub” the old site (customer data) to which the server was allocated, to reboot the server and to load the new site to which the server has been allocated. The length of the time interval is set to be equal to the non-negligible amount of time required for a server to prepare to serve a new customer. In current technology, this time is in the order of 5 or 10 minutes. [0011] Each server has a rate of requests it can serve in a time interval. For simplicity, all rates are assumed to be identical. Due to practical concerns (mainly security constraints placed by customers), sharing of servers at the same time is not allowed. That is, customers share servers only in the sense of using the same servers at different times, but do not use the same servers at the same time. Thus, even in case of overload, some of the servers may be underutilized if they are allocated to sites with rates of requests lower than the servers' rate. [0012] Each customer's demand is assumed to be associated with a benefit gained by the service provider in case a unit demand is satisfied. Given a fixed number of servers, the objective of the service provider is to find a time-varying server allocation that would yield benefit gained by satisfying sites' demand. Since in the problem solved by the present invention future demand of the sites is known, a polynomial time algorithm is used to compute the optimal offline allocation. [0013] Interestingly, the model can be cast as a more general benefit task system. In this task system, we are given a set of states for each time, t, and a benefit function. The system can be at a single state at each time, and the benefit for time t is a function of the system states at times t−1 and t. The goal is to find a time varying sequence of states that yields benefit. That is, at each time t, we need to determine to which state should the system move (and this will be the state of the system at time t+1), and we gain the benefit that is determined by the benefit function. Similar to the server farm model, the benefit function is known in advance. [0014] It can be shown that benefit task systems capture also benefit maximization variants of well studied problems, such as the k-server problem (see A. Borodin and R. El-Yaniv in [0015] The foregoing and other objects, aspects and advantages will be better understood from the following detailed description of a preferred embodiment of the invention with reference to the drawings, in which: [0016]FIG. 1 is a block diagram illustrating the architecture of a Web server farm; [0017]FIG. 2 is a flow diagram illustrating the process of allocating servers using projected future benefits; [0018]FIG. 3 is a network flow graph showing the special case of two customers and two time steps; [0019]FIG. 4 is a detail illustrating the edges corresponding to a single customer for a single time step; and [0020]FIG. 5 is a flow diagram illustrating the process of computing new allocations of servers. [0021] Although the invention is described in terms of a specific application to a Web server farm, this explanation is by way of example only. It will be understood by those skilled in the art that the invention may be applied to other applications. Among those applications are the customer telephone support problem and the allocation of computers to computationally intensive problems already mentioned. The Web server farm problem will serve to provide a concrete application of the invention which can be applied to other resource allocation problems. [0022] Referring now to the drawings, and more particularly to FIG. 1, there is shown, in generalized form, the architecture of a Web server farm of the type managed and maintained by a Web hosting service provider. The farm itself comprises a plurality of servers [0023]FIG. 2 illustrates the general process implemented by the dynamic resource allocator [0024] The first function block [0025] Suppose that we are given s Web sites that are to be served by k Web servers. (For simplicity, we assume that all servers are identical.) Time is divided into units. It is assumed that the demand of a Web site is uniform in each time unit. Each server has a “service rate” which is the number of requests to a Web site each server can serve in a time unit. Without loss of generality, we normalize the demands by the service rate so that a server can serve one request per time unit and demands of a site may be fractional. A Web server can be allocated to no more than one site at each time unit and it takes a time unit to change the allocation of a server. [0026] A problem instance consists of the number of servers, k, the number of sites, s, a non-negative benefit matrix, b [0027] of the servers allocated to site i for the time step t are “productive”, i.e., actually serve requests. We get that the total benefit of an allocation {a [0028] In the offline solution of this problem according to the present invention, we are given the complete demand matrix, {d [0029] The Web server farm problem is a special case of the generalized task system benefit problem. In this problem, we are given (i) a set of possible states U [0030] In the offline version of the problem, all the state sets and the benefit function are known in advance. [0031] Observe that the Web server farm problem can be cast in this setting by identifying each possible allocation of servers to sites at time t with a state S [0032] The offline Web server farm problem can be solved in polynomial-time. We reduce the Web server farm problem to the well-known minimum-cost network flow problem, which can be solved in polynomial time. See, for example, R. K. Ahuja, T. L. Magnanti and J. B. Orlin, [0033] Theorem 1. The offline Web server problem can be reduced in polynomial time to a minimum-cost network flow problem. Hence, it can be solved in polynomial time. [0034] Proof. Recall that the input for the minimum cost network flow problem is a directed network, two special vertices called the source vertex and the sink vertex, an amount of flow to be injected to the source vertex, and a non-negative capacity and a cost for each edge. The goal is to find from all the flows from s to t that respect the edge capacities and are of size k, one that has a minimal cost, where the cost of a flow is the sum, over all edges, of the product of the flow on the edge and its cost. [0035] In fact, we describe below a reduction from the Web server farm problem to the analogous maximum-cost network flow problem. The latter problem is essentially the same as the minimum-cost network flow problem (and thus can be solved in polynomial time), since the edge costs are not restricted in sign, i.e., they are allowed to be negative. We remark that in our network, all the paths from s to t are of equal length, and therefore another way to guarantee that all costs are non-negative is to increase the costs of all the edges by the same sufficiently large number. [0036] The outline of the reduction is illustrated in FIG. 3. Given the instance of the Web server farm problem, we construct a (directed) network with s “rails”, one per site. Each rail is a chain of edges each representing one time step. (Actually, we will split these edges into three parallel edges, for reasons which will become clear shortly.) Flow along a rail represents the allocation of servers to the corresponding site. In addition, we construct a set of “free pool” nodes, one per time step, through which flow will pass when servers are reallocated from one site to another. [0037] Let d [0038] We also construct edges of infinite capacity and cost zero from n [0039] Finally, we construct a source into which we inject flow k, with infinite capacity zero cost edges to each n [0040] It is not hard to see that an integral flow of cost C in this network corresponds to an allocation {a [0041] Returning now to the drawings, the computation of new allocations (function block [0042] While the invention has been described in terms of a preferred embodiment, those skilled in the art will recognize that the invention can be practiced with modification within the spirit and scope of the appended claims. Referenced by
Classifications
Legal Events
Rotate |